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The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed splitting. We discuss far-field splitting in the full field and near-horizon splitting in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the splitting behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field splitting is explained by competition between projected modes. The near-horizon splitting is due to excitation of lower multipole modes that back excite the multipole mode for which splitting is observed. In both cases splitting is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter--mode excitation effect that we study.
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Outside a black hole, perturbation fields die off in time as $1/t^n$. For spherical holes $n=2ell+3$ where $ell$ is the multipole index. In the nonspherical Kerr spacetime there is no coordinate-independent meaning of multipole, and a common sense viewpoint is to set $ell$ to the lowest radiatiable index, although theoretical studies have led to very different claims. Numerical results, to date, have been controversial. Here we show that expansion for small Kerr spin parameter $a$ leads to very definite numerical results confirming previous theoretical analyses.
The gravitational wave measurements of spin-induced multipole moment coefficients of a binary black hole system can be used to distinguish black holes from other compact objects [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we apply the idea proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)] to binary systems composed of intermediate-mass and supermassive black holes and derive the expected bounds on their Kerr nature using future space-based gravitational wave detectors. Using astrophysical models of binary black hole population, we study the measurability of the spin-induced quadrupole and octupole moment coefficients using LISA and DECIGO. The errors on spin-induced quadrupole moment parameter of the binary system are found to be { $leq 0.1$ for almost $3%$ of the total supermassive binary black hole population which is detectable by LISA whereas it is $sim 46%$ for the intermediate-mass black hole binaries observable by DECIGO at its design sensitivity.} We find that { errors on} {it both} the quadrupole and octupole moment parameters can be estimated to { be} $leq 1$ for $sim 2%$ and $sim 50%$ {of the population} respectively for LISA and DECIGO detectors. { Our findings suggest that a subpopulation of binary black hole events, with the signal to noise ratio thresholds greater than 200 and 100 respectively for LISA and DECIGO detectors, would permit tests of black hole nature to 10% precision.}
We classify radial timelike geodesic motion of the exterior non-extremal Kerr spacetime by performing a taxonomy of inequivalent root structures of the first order radial geodesic equation using a novel compact notation and by implementing the constraints from polar, time and azimuthal motion. Four generic root structures with only simple roots give rise to eight non-generic root structures when either one root becomes coincident with the horizon, one root vanishes or two roots becomes coincident. We derive the explicit phase space of all such root systems in the basis of energy, angular momentum and Carters constant and classify whether each corresponding radial geodesic motion is allowed or disallowed from existence of polar, time and azimuthal motion. The classification of radial motion within the ergoregion for both positive and negative energies leads to 6 distinguished values of the Kerr angular momentum. The classification of null radial motion and near-horizon extremal Kerr radial motion are obtained as limiting cases and compared with the literature. We explicitly parametrize the separatrix describing root systems with double roots as the union of the following three regions that are described by the same quartic respectively obtained when (1) the pericenter of bound motion becomes a double root; (2) the eccentricity of bound motion becomes zero; (3) the turning point of unbound motion becomes a double root.
We introduce a family of solutions of Einsteins gravity minimally coupled to an anisotropic fluid, describing asymptotically flat black holes with hair and a regular horizon. These spacetimes can describe the geometry of galaxies harboring supermassive black holes, and are extensions of Einstein clusters to include horizons. They are useful to constrain the environment surrounding astrophysical black holes, using electromagnetic or gravitational-wave observations. We compute the main properties of the geometry, including the corrections to the ringdown stage induced by the external matter and fluxes by orbiting particles. The leading order effect to these corrections is a gravitational-redshift, but gravitational-wave propagation is affected by the galactic potential in a nontrivial way, and may be characterized with future observatories.
Context. The Event Horizon Telescope (EHT) collaboration recently obtained first images of the surroundings of the supermassive compact object M87* at the center of the galaxy M87. Aims. We want to develop a simple analytic disk model for the accretion flow of M87*. Compared to general-relativistic magnetohydrodynamic (GRMHD) models, it has the advantage of being independent of the turbulent character of the flow, and controlled by only few easy-to-interpret, physically meaningful parameters. We want to use this model to predict the image of M87* assuming that it is either a Kerr black hole, or an alternative compact object. Methods. We compute the synchrotron emission from the disk model and propagate the resulting light rays to the far-away observer by means of relativistic ray tracing. Such computations are performed assuming different spacetimes (Kerr, Minkowski, non-rotating ultracompact star, rotating boson star or Lamy spinning wormhole). We perform numerical fits of these models to the EHT data. Results. We discuss the highly-lensed features of Kerr images and show that they are intrinsically linked to the accretion-flow properties, and not only to gravitation. This fact is illustrated by the notion of secondary ring that we introduce. Our model of spinning Kerr black hole predicts mass and orientation consistent with the EHT interpretation. The non-Kerr images result in similar quality of the numerical fits and may appear very similar to Kerr images, once blurred to the EHT resolution. This implies that a strong test of the Kerr spacetime may be out of reach with the current data. We notice that future developments of the EHT could alter this situation. Conclusions. Our results show the importance of studying alternatives to the Kerr spacetime in order to be able to test the Kerr paradigm unambiguously.
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